Jules Tannery

Jules Tannery (24 March 1848 – 11 December 1910) was a French mathematician, brother of the mathematician and historian of science Paul Tannery, who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard. Tannery's theorem on interchange of limits and series is named after him.[1]

Jules Tannery
Jules Tannery (1848-1910). Photo by A. Gerschel & Sons (c. 1866).
Born(1848-03-24)24 March 1848
Died11 December 1910(1910-12-11) (aged 62)
Alma materÉcole Normale Supérieure
Known forPhilosophy of mathematics
Scientific career
InstitutionsÉcole Normale Supérieure
Université de Paris
Doctoral advisorCharles Hermite
Doctoral studentsAlbert Châtelet
Jacques Hadamard
InfluencedPaul Tannery
Paul Painlevé
Jules Drach
Émile Borel
Élie Cartan
Brother of Paul Tannery

Under Hermite, he received is doctorate in 1874 for his thesis Propriétés des Intégrales des Équations Différentielle Linéaires à Coefficients Variables.

Tannery was an advocate for mathematics education, particular as a means to train children in logical consequence through synthetic geometry and mathematical proofs.[2]

Tannery discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think."

He notably influenced Pierre Duhem, Paul Painlevé, Jules Drach, and Émile Borel to take up science.

His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking. Tannery was "an original thinker, a successful teacher, and a writer endowed with an unusually clear, brilliant and attractive style."[3]



  1. Hofbauer, Josef (2002). "A Simple Proof of 1 + 1/22 + 1/32 + ⋯ = π2/6 and Related Identities". The American Mathematical Monthly. 109 (2): 196–200. doi:10.2307/2695334. JSTOR 2695334.
  2. Jules Tannery The Teaching of Elementary Geometry via Pacific Institute for the Mathematical Sciences
  3. G. B. Mathews (1910) Jules Tannery Nature 85:175 (#2145)
  • George Sarton (1947) "Paul, Jules, and Marie Tannery (with a note on Grégoire Wyrouboff)", Isis 38 (1/2): 33–51.
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